Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Пеньковский В.И.   Корсакова Н.К.  

Modeling processes of the diapir and frozen earth massif ablation in the ground water flow

Reporter: Пеньковский В.И.

A mathematical model of mass loss from surfaces of impermeable massifs of rock salt (diapir, for example), closed frozen earth inclusions or icebergs in potential flow are proposed. The phenomenon of the mass elimination (ablation) from the surface of massif and the heat gain to melting massif are governed by the same convective-diffusion laws. Under these circumstances a relation between convective and diffusive mass or heat transfer components is different in various flow regions. The diffusive process predominates in the boundary layer (at small Pecle numbers) while the convective process predominates in the rest region of flow. The value of heat (or mass) transfer is directly proportional to the diffusive coefficient, difference between temperature (or mass concentration) by surface body and temperature (or mass concentration) in incoming flow, and the same value is inversely proportional to the boundary layer thickness. In many cases we can assume that the thickness of the layer is inversely proportional to the velocity of flow about the body. This assumption, coupled with impermeability condition, leads to the linear relation between the normal flow velocity and the tangent flow velocity on timely changing surface of massif.
The two-dimensional potential flow cases, for which one can write some analytical solutions, are considered. Generally, the finite-element method is applied.
The experimental arrangement has been constructed. The preliminary experiments have conducted. The results of the preliminary experiments are agreed qualitatively with the numerical results.

Abstracts file: Тез НИКНИК.Doc
Full text file: Penkovskii.doc


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